Non-Boolean computations implementing operations on multi-valued variables beyond base 2 allow enhanced computational complexity. We introduce DNA as a functional material for ternary computing, and in particular demonstrate the use of three-valued oligonucleotide inputs to construct a 3 [times] 3 multiplication table. The system consists of two three-valued inputs of -1; 0; +1 and a fluorophore/quencher functional hairpin acting as computational and reporter module. The interaction of the computational hairpin module with the different values of the inputs yields a 3 [times] 3 multiplication matrix consisting of nine nanostructures that are read out by three distinct fluorescence intensities. By combining three different hairpin computational modules, each modified with a different fluorophore/quencher pair, and using different sets of inputs, the parallel operation of three multiplication tables is demonstrated. [less ▲]

To understand how pairwise cellular interactions influence cellular architectures, we measured the levels of functional proteins associated with EGF receptor (EGFR) signaling in pairs of U87EGFR variant III oncogene receptor cells (U87EGFRvIII) at varying cell separations. Using a thermodynamics-derived approach we analyzed the cell-separation dependence of the signaling stability, and identified that the stable steady state of EGFR signaling exists when two U87EGFRvIII cells are separated by 80–100 μm. This distance range was verified as the characteristic intercellular separation within bulk cell cultures. EGFR protein network signaling coordination for the U87EGFRvIII system was lowest at the stable state and most similar to isolated cell signaling. Measurements of cultures of less tumorigenic U87PTEN cells were then used to correctly predict that stable EGFR signaling occurs for those cells at smaller cell–cell separations. The intimate relationship between functional protein levels and cellular architectures explains the scattered nature of U87EGFRvIII cells relative to U87PTEN cells in glioblastoma multiforme tumors. [less ▲]

In nature, post-transcriptional alternative splicing processes expand the proteome biodiversity, providing means to synthesize various protein isoforms. We describe the input-guided assembly of a DNAzyme-based full-adder computing system, which mimics functions of the natural processes by increasing the diversity of logic elements by the reconfiguration of the inputs. The full-adder comprises the simultaneous operation of three inputs that yield two different output signals, acting as sum and carry bits. The DNAzyme-based full-adder system consists of a library of Mg2+-dependent DNAzyme subunits and their substrates that are modified by two different fluorophore/quencher pairs that encode the sum and carry outputs. The input-guided assembly of DNAzyme subunits, formed by three inputs composed of nucleic acid hairpin structures, leads to computing modules that yield the sum and carry outputs of the full-adder. In the presence of a single input the DNAzyme computing module yields the sum fluorescence output. In the presence of two of the inputs, the reconfiguration of the input structures proceeds, leading to an input-guided computing module that yields the carry fluorescence output. By introducing all the three inputs the sequential inter-input hybridization leads to the reconfiguration of the inputs into polymer wires. These include binding sites for two types of DNAzyme and their substrates leading to the carry and sum fluorescence outputs. The advantages of the simultaneous three-input operation of the full-adder and the possibilities to implement DNAzyme-based computing modules for cascading full-adders are discussed. [less ▲]

in Proceedings of the National Academy of Sciences (2013), 110(43), 17183-17188

The outcome of a light–matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of ... [more ▼]

The outcome of a light–matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of a time-varying system requires measuring an (ideally complete) set of time-dependent observables. Typically, this is prohibitive, but in weak-field spectroscopy we can move toward this goal because only a finite number of levels are accessible. Recent progress in nonlinear spectroscopies means that nontrivial measurements can be implemented and thereby give rise to interesting logic schemes where the outputs are functions of the observables. Lie algebra offers a natural tool for generating the outcome of the bilinear light–matter interaction. We show how to synthesize these ideas by explicitly discussing three-photon spectroscopy of a bichromophoric molecule for which there are four accessible states. Switching logic would use the on–off occupancies of these four states as outcomes. Here, we explore the use of all 16 observables that define the time-evolving state of the bichromophoric system. The bilinear laser–system interaction with the three pulses of the setup of a 2D photon echo spectroscopy experiment can be used to generate a rich parallel logic that corresponds to the implementation of a molecular decision tree. Our simulations allow relaxation by weak coupling to the environment, which adds to the complexity of the logic operations. [less ▲]

in Proceedings of the National Academy of Sciences (2013), 110(47), 19160-19165

Toward identifying a cancer-specific gene signature we applied surprisal analysis to the RNAs expression behavior for a large cohort of breast, lung, ovarian, and prostate carcinoma patients. We ... [more ▼]

Toward identifying a cancer-specific gene signature we applied surprisal analysis to the RNAs expression behavior for a large cohort of breast, lung, ovarian, and prostate carcinoma patients. We characterize the cancer phenotypic state as a shared response of a set of mRNA or microRNAs (miRNAs) in cancer patients versus noncancer controls. The resulting signature is robust with respect to individual patient variability and distinguishes with high fidelity between cancer and noncancer patients. The mRNAs and miRNAs that are implicated in the signature are correlated and are known to contribute to the regulation of cancer-signaling pathways. The miRNA and mRNA networks are common to the noncancer and cancer patients, but the disease modulates the strength of the connectivities. Furthermore, we experimentally assessed the cancer-specific signatures as possible therapeutic targets. Specifically we restructured a single dominant connectivity in the cancer-specific gene network in vitro. We find a deflection from the cancer phenotype, significantly reducing cancer cell proliferation and altering cancer cellular physiology. Our approach is grounded in thermodynamics augmented by information theory. The thermodynamic reasoning is demonstrated to ensure that the derived signature is bias-free and shows that the most significant redistribution of free energy occurs in programming a system between the noncancer and cancer states. This paper introduces a platform that can elucidate miRNA and mRNA behavior on a systems level and provides a comprehensive systematic view of both the energetics of the expression levels of RNAs and of their changes during tumorigenicity. [less ▲]

in Proceedings of the National Academy of Sciences (2012), 109(52), 21228-21233

The Toffoli and Fredkin gates were suggested as a means to exhibit logic reversibility and thereby reduce energy dissipation associated with logic operations in dense computing circuits. We present a ... [more ▼]

The Toffoli and Fredkin gates were suggested as a means to exhibit logic reversibility and thereby reduce energy dissipation associated with logic operations in dense computing circuits. We present a construction of the logically reversible Toffoli and Fredkin gates by implementing a library of predesigned Mg2+-dependent DNAzymes and their respective substrates. Although the logical reversibility, for which each set of inputs uniquely correlates to a set of outputs, is demonstrated, the systems manifest thermodynamic irreversibility originating from two quite distinct and nonrelated phenomena. (i) The physical readout of the gates is by fluorescence that depletes the population of the final state of the machine. This irreversible, heat-releasing process is needed for the generation of the output. (ii) The DNAzyme-powered logic gates are made to operate at a finite rate by invoking downhill energy-releasing processes. Even though the three bits of Toffoli’s and Fredkin’s logically reversible gates manifest thermodynamic irreversibility, we suggest that these gates could have important practical implication in future nanomedicine. [less ▲]